This will never happen due to massive cost a Shuttle needs for operation. A private company will pursue financial profit and the Shuttle is anything but financially profitable. It would have been if the initial projection of 60 flights/year were a reality, but that never happened and never will. Ad this to decaying infrastructure (no more ET being build) and personnel layoffs. If the remaining Shuttle mission will be successful, their place should be in museums. They've done their job, bringing Man into orbit and building the ISS. Don't push their luck, a Shuttle is a very, very fragile system and only very skilled men a huge amount of luck made it possible to fly so many missions with only two total failures.
As for the plans for a new shuttle, it's futile as long as we don't have a clear destination for it. The STS program was intended for LEO, not GEO, not Moon flyby, no Mars landing. We've been to LEO, we already have a huge space station there, let's go further. Makes no sense to have a shuttle fly astronauts to asteroids or Mars.
Don't get me wrong, I love the Shuttle. It's a brilliant flying machine and she did a really good job. But it's time for a new vehicle.